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Introduce inverse hyperbolic functions

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#KT-4900

Improve accuracy of JS polyfills of hyperbolic functions and expm1/log1p
This commit is contained in:
Ilya Gorbunov
2017-08-30 21:00:30 +03:00
parent 232d1bd9ef
commit 044ccf1532
10 changed files with 634 additions and 29 deletions
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js/js.libraries/src/core/js.math.kt
+6
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@@ -62,6 +62,12 @@ public external object Math {
internal fun cosh(value: Double): Double
@PublishedApi
internal fun tanh(value: Double): Double
@PublishedApi
internal fun asinh(value: Double): Double
@PublishedApi
internal fun acosh(value: Double): Double
@PublishedApi
internal fun atanh(value: Double): Double
@PublishedApi
internal fun hypot(x: Double, y: Double): Double
js/js.libraries/src/core/math.kt
+92
View File
@@ -152,6 +152,52 @@ public inline fun cosh(a: Double): Double = nativeMath.cosh(a)
@InlineOnly
public inline fun tanh(a: Double): Double = nativeMath.tanh(a)
/**
* Computes the inverse hyperbolic sine of the value [a].
*
* The returned value is `x` such that `sinh(x) == a`.
*
* Special cases:
*
* - `asinh(NaN)` is `NaN`
* - `asinh(+Inf)` is `+Inf`
* - `asinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun asinh(a: Double): Double = nativeMath.asinh(a)
/**
* Computes the inverse hyperbolic cosine of the value [a].
*
* The returned value is positive `x` such that `cosh(x) == a`.
*
* Special cases:
*
* - `acosh(NaN)` is `NaN`
* - `acosh(x)` is `NaN` when `x < 1`
* - `acosh(+Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun acosh(a: Double): Double = nativeMath.acosh(a)
/**
* Computes the inverse hyperbolic tangent of the value [a].
*
* The returned value is `x` such that `tanh(x) == a`.
*
* Special cases:
*
* - `tanh(NaN)` is `NaN`
* - `tanh(x)` is `NaN` when `x > 1` or `x < -1`
* - `tanh(1.0)` is `+Inf`
* - `tanh(-1.0)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun atanh(a: Double): Double = nativeMath.atanh(a)
/**
* Computes `sqrt(x^2 + y^2)` without intermediate overflow or underflow.
*
@@ -592,6 +638,52 @@ public inline fun cosh(a: Float): Float = nativeMath.cosh(a.toDouble()).toFloat(
@InlineOnly
public inline fun tanh(a: Float): Float = nativeMath.tanh(a.toDouble()).toFloat()
/**
* Computes the inverse hyperbolic sine of the value [a].
*
* The returned value is `x` such that `sinh(x) == a`.
*
* Special cases:
*
* - `asinh(NaN)` is `NaN`
* - `asinh(+Inf)` is `+Inf`
* - `asinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun asinh(a: Float): Float = nativeMath.asinh(a.toDouble()).toFloat()
/**
* Computes the inverse hyperbolic cosine of the value [a].
*
* The returned value is positive `x` such that `cosh(x) == a`.
*
* Special cases:
*
* - `acosh(NaN)` is `NaN`
* - `acosh(x)` is `NaN` when `x < 1`
* - `acosh(+Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun acosh(a: Float): Float = nativeMath.acosh(a.toDouble()).toFloat()
/**
* Computes the inverse hyperbolic tangent of the value [a].
*
* The returned value is `x` such that `tanh(x) == a`.
*
* Special cases:
*
* - `tanh(NaN)` is `NaN`
* - `tanh(x)` is `NaN` when `x > 1` or `x < -1`
* - `tanh(1.0)` is `+Inf`
* - `tanh(-1.0)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun atanh(a: Float): Float = nativeMath.atanh(a.toDouble()).toFloat()
/**
* Computes `sqrt(x^2 + y^2)` without intermediate overflow or underflow.
*
js/js.libraries/src/js/polyfills.js
+166 -28
View File
@@ -52,24 +52,171 @@ if (typeof Math.trunc === "undefined") {
return Math.ceil(x);
};
}
if (typeof Math.sinh === "undefined") {
Math.sinh = function(x) {
var y = Math.exp(x);
return (y - 1 / y) / 2;
};
}
if (typeof Math.cosh === "undefined") {
Math.cosh = function(x) {
var y = Math.exp(x);
return (y + 1 / y) / 2;
};
}
if (typeof Math.tanh === "undefined") {
Math.tanh = function(x){
var a = Math.exp(+x), b = Math.exp(-x);
return a == Infinity ? 1 : b == Infinity ? -1 : (a - b) / (a + b);
};
}
(function() {
var epsilon = 2.220446049250313E-16;
var taylor_2_bound = Math.sqrt(epsilon);
var taylor_n_bound = Math.sqrt(taylor_2_bound);
var upper_taylor_2_bound = 1/taylor_2_bound;
var upper_taylor_n_bound = 1/taylor_n_bound;
if (typeof Math.sinh === "undefined") {
Math.sinh = function(x) {
if (Math.abs(x) < taylor_n_bound) {
var result = x;
if (Math.abs(x) > taylor_2_bound) {
result += (x * x * x) / 6;
}
return result;
} else {
var y = Math.exp(x);
var y1 = 1 / y;
if (!isFinite(y)) return Math.exp(x - Math.LN2);
if (!isFinite(y1)) return -Math.exp(-x - Math.LN2);
return (y - y1) / 2;
}
};
}
if (typeof Math.cosh === "undefined") {
Math.cosh = function(x) {
var y = Math.exp(x);
var y1 = 1 / y;
if (!isFinite(y) || !isFinite(y1)) return Math.exp(Math.abs(x) - Math.LN2);
return (y + y1) / 2;
};
}
if (typeof Math.tanh === "undefined") {
Math.tanh = function(x){
if (Math.abs(x) < taylor_n_bound) {
var result = x;
if (Math.abs(x) > taylor_2_bound) {
result -= (x * x * x) / 3;
}
return result;
}
else {
var a = Math.exp(+x), b = Math.exp(-x);
return a === Infinity ? 1 : b === Infinity ? -1 : (a - b) / (a + b);
}
};
}
// Inverse hyperbolic function implementations derived from boost special math functions,
// Copyright Eric Ford & Hubert Holin 2001.
if (typeof Math.asinh === "undefined") {
var asinh = function(x) {
if (x >= +taylor_n_bound)
{
if (x > upper_taylor_n_bound)
{
if (x > upper_taylor_2_bound)
{
// approximation by laurent series in 1/x at 0+ order from -1 to 0
return Math.log(x) + Math.LN2;
}
else
{
// approximation by laurent series in 1/x at 0+ order from -1 to 1
return Math.log(x * 2 + (1 / (x * 2)));
}
}
else
{
return Math.log(x + Math.sqrt(x * x + 1));
}
}
else if (x <= -taylor_n_bound)
{
return -asinh(-x);
}
else
{
// approximation by taylor series in x at 0 up to order 2
var result = x;
if (Math.abs(x) >= taylor_2_bound)
{
var x3 = x * x * x;
// approximation by taylor series in x at 0 up to order 4
result -= x3 / 6;
}
return result;
}
};
Math.asinh = asinh;
}
if (typeof Math.acosh === "undefined") {
Math.acosh = function(x) {
if (x < 1)
{
return NaN;
}
else if (x - 1 >= taylor_n_bound)
{
if (x > upper_taylor_2_bound)
{
// approximation by laurent series in 1/x at 0+ order from -1 to 0
return Math.log(x) + Math.LN2;
}
else
{
return Math.log(x + Math.sqrt(x * x - 1));
}
}
else
{
var y = Math.sqrt(x - 1);
// approximation by taylor series in y at 0 up to order 2
var result = y;
if (y >= taylor_2_bound)
{
var y3 = y * y * y;
// approximation by taylor series in y at 0 up to order 4
result -= y3 / 12;
}
return Math.sqrt(2) * result;
}
};
}
if (typeof Math.atanh === "undefined") {
Math.atanh = function(x) {
if (Math.abs(x) < taylor_n_bound) {
var result = x;
if (Math.abs(x) > taylor_2_bound) {
result += (x * x * x) / 3;
}
return result;
}
return Math.log((1 + x) / (1 - x)) / 2;
};
}
if (typeof Math.log1p === "undefined") {
Math.log1p = function(x) {
if (Math.abs(x) < taylor_n_bound) {
var x2 = x * x;
var x3 = x2 * x;
var x4 = x3 * x;
// approximation by taylor series in x at 0 up to order 4
return (-x4 / 4 + x3 / 3 - x2 / 2 + x);
}
return Math.log(x + 1);
};
}
if (typeof Math.expm1 === "undefined") {
Math.expm1 = function(x) {
if (Math.abs(x) < taylor_n_bound) {
var x2 = x * x;
var x3 = x2 * x;
var x4 = x3 * x;
// approximation by taylor series in x at 0 up to order 4
return (x4 / 24 + x3 / 6 + x2 / 2 + x);
}
return Math.exp(x) - 1;
};
}
})();
if (typeof Math.hypot === "undefined") {
Math.hypot = function() {
var y = 0;
@@ -94,16 +241,7 @@ if (typeof Math.log2 === "undefined") {
return Math.log(x) * Math.LOG2E;
};
}
if (typeof Math.log1p === "undefined") {
Math.log1p = function(x) {
return Math.log(x + 1);
};
}
if (typeof Math.expm1 === "undefined") {
Math.expm1 = function(x) {
return Math.exp(x) - 1;
};
}
// For HtmlUnit and PhantomJs
if (typeof ArrayBuffer.isView === "undefined") {
ArrayBuffer.isView = function(a) {